Model calibration
The difference of each measured sampling point (ti)with
the modelled data was made. This was done for every component and for
every measured data point. All the obtained differences were squared and
summed to obtained the sum of squared errors (SSE) as shown in equation
A-2.
\begin{equation}
\text{SS}E_{j}=\sum_{i=1}^{N}\left(n_{j}^{\text{measure}}\left(t_{i}\right)-n_{j}^{\text{model}}\left(t_{i}\right)\right)^{2}(A-2)\nonumber \\
\end{equation}- j= glucose, aceate, propionate, butyrate, lactate, SP, biomass
- i= time corresponding to each measured data point
- njmeasured = the amount of compound
j measured [gCOD]
- njmodel = the modelled amount of
compound j [gCOD]
Subsequently the SSE of each component was summated to each other
obtaining the total error of the model. The VSS was not taken into
account for the SSE, as the SRT was significantly longer than the HRT
the quantification of VSS was assumed not to be accurate within one
cycle. The SSE was obtained as follows (eq. A-3):
\(Total\ error=\ \sum{\text{SS}E_{j}}\ (A-3)\)
The total error was minimized adjusting characteristic parameters e.g.,
qSmax, KSP, KLac,
KGlu and the yields shown in table A.1, done by the
solver tool of Microsoft Excel. The solver was used to obtain the
minimal total error, and the solver was set at GRG non-linear method. No
additional constraints were made for the model then the constraints
mentioned before. The intial yields used were 0.5
gCOD·gCOD-1, KSP was initially 0.01
min-1 and an initial qSmax of 1
gCOD·gVSS-1·h-1.